Introduction
Metamaterials, with the subwavelength scale unit cell, have attracted intense attention due to their exotic properties that are unavailable in nature, such as invisibility cloaking [ 1], perfect lensing [ 2] and negative index of refraction [ 3]. Split ring resonators (SRRs) [ 4], fishnet structures [ 5], cut wire pairs [ 6] and other stereostructures [ 7] have been proposed for the landmark predictions of metamaterial theory. Among them, the SRRs are the most frequently used structures for achieving the exotic properties of the metamaterials. The working principle of the SRRs can be understood in terms of electrical engineering. The gap and ring of the SRRs represent the equivalent capacitance (C) and inductance (L) [ 8], respectively. They together constitute an LC circuit, coupled to an external electric field, and an appropriate resonance frequency can be obtained.
The features of easy fabrication and engineered response make the SRRs very attractive from the perspective of device. Different structure based on the SRRs, such as electric SRRs (eSRRs) [ 9], nested SRRs [ 10– 12], active tunable SRRs [ 13] and reconfigurable SRRs [ 14], were proposed by other groups, and they have greatly promoted the development of the metamaterials field. Meanwhile, various metamaterial devices like filters [ 15], modulators [ 16], absorbers [ 17– 19] and switches [ 20] have been also successfully demonstrated. However, most metamaterial designs up to date exhibit narrow-band electromagnetic response because of the resonant nature of the SRR-based metamaterials, which limits their performance for broadband applications [ 21– 26].
An effective method to broaden the resonance bandwidth of the SRRs is to make the metamaterial units resonate at several neighboring frequencies. Following this design strategy, broadband SRRs have been demonstrated in relevant spectral ranges including microwaves, terahertz, infrared and optical frequencies [ 21– 26]. For example, Han et al. [ 21] presented the broadband terahertz metamaterial by stacking five different sized SRRs. However, the proposal suffers from one crucial drawback, namely that in the fabrication it is quite difficult to exactly align the relative position of each patterned metallic structure, in particular at higher frequencies such as terahertz, infrared and visible regions. Therefore, it is necessary to develop the broadband coplane metamaterial structure.
Very recently, two significant advancements in designing the coplane broadband filters by combing several (no less than 3) SRRs with different size in a unit cell have been demonstrated by Rigi-Tamandani et al. [ 27] and Han et al. [ 28]. These proposed structures, however, to some extent have their own complexities in fabrication and the bandwidth is not apparent broadening (2.5 times in Ref. [ 28]. and only 1.7 times in Ref. [ 27].). Hence, metamaterial structures of simple schematics which can provide a large resonance bandwidth are necessary.
Herein, we proposed a novel broadband coplane terahertz metamaterial filter formed by two nested U-shaped SRRs. Compared with the bandwidth of the outer SRR, the bandwidth of the structure gradually increased with the decrease of the arm length of the inner SRR, and finally a 7.4 times bandwidth broadening was obtained. The broadening of the resonance bandwidth resulted from the increase in the radiation of the entire structure. Furthermore, a further bandwidth broadening can be obtained by decreasing the period of the structure. The results of the proposed structure appear to be very promising for broadband cloaking devices and band-stop filters.
Structure and design
The unit cell of the structure is illustrated in Fig. 1. It consists of two U-shaped SRRs. The separation between the two SRRs was fixed at s1 = 12 mm, while the length s2 along the y-axis direction form an arithmetic series (from original s2 = 4 to 28 mm), and the difference = 4 mm. The period of this structure was P = Px = Py = 85 mm, the thickness of the metal (Au) was 0.4 mm with a frequency independent conductivity of s = 4.09×107 S/m. The width of those two SRRs was w = 4 mm, and the gap between them was g = 4 mm. The length of the outer SRR was l = 45 mm. The proposed structure was placed on a glass substrate with an electrical permittivity of 2.25. Our results were obtained through finite-difference time-domain (FDTD) simulations, where the periodic structures were illuminated by a normally incident plane wave with the electric field parallel to the x-axis. Perfectly matched layers were applied along the z direction and periodic boundary conditions were set in the x and y directions.
Simulation results and discussion
Figure 2 shows the normalized transmission spectra of the proposed structure. It is obvious that the resonance bandwidth (i.e., the full width at half maximum) of the structure gradually increased with the decrease of the s2. The broadening of the bandwidth is 107 GHz from the original outer SRR to s2 = 4 mm, 33.5 GHz from s2 = 4 to 8 mm, 46.8 GHz from s2 = 8 to 12 mm, 53.6 GHz from s2 = 12 to 16 mm, 60.2 GHz from s2 = 16 to 20 mm, 66.9 GHz from s2 = 20 to 24 mm and 60.2 GHz from s2 = 24 to 28 mm. Compared with the original SRR, the resonance bandwidth in s2 = 28 mm gets enhanced by about 7.4 times. Additionally, the shift of the frequency was about 0.94 THz.
To reveal the physical origin of the broadening of the resonance bandwidth, Figs. 3 and 4 show the calculated electric (|E|) and magnetic (|Hz|) field distributions corresponding to the respective transmission dips at s2 = 4, 8, and 12 mm and s2 = 20, 24, and 28 mm, respectively. The broadening of the resonance bandwidth resulted from two different resonance mechanisms. One is that the loop current redistribution reduce effective inductance which is responsible for the bandwidth broadening and resonance blue shifting [ 15, 16], the other is less magnetic resonance or more radiation damping.
For s2 = 4, 8, and 12 mm, the distributions of the electrical (|E|) field was mainly concentrated on the gap of the structure (see Figs. 3(a1)–3(c1)). It is well known that the distribution of the magnetic field is associated with the excitation of a loop current along the SRR arms. As shown in Figs. 3(a2)–3(c2), it is obvious that there were two induced parallel path currents for s2 = 4, 8 and 12 mm, respectively. Therefore, the effective inductance originating from each induced loop currents along the metal arms lowers the effective inductance of the entire structure due to their parallel connection [ 15, 16]. Besides, due to the constant geometry of the gap, the resonance response changes are mainly determined by the variation of effective inductance. According to the LC circuit model [ 12], it is easy to understand the changes in the resonance bandwidth and blue shift when the effective inductance is decreased. In particular, we also observed that the induced loop current was mainly concentrated in the inner SRR of the designed structure (see the distributions of the magnetic field in Figs. 3(a2)–3(c2)). Hence, the dramatic increases in resonance bandwidth and the blue shift are mainly attributed to the decrease in effective inductance of the inner SRR. Although its resonance bandwidth can be further broaden when we further decrease the arm length of the inner SRR (s2 = 20, 24, and 28 mm), the mechanism of the broadened bandwidth is different from the case of the s2 = 4, 8, and 12 mm.
In order to understand the physical originals of further broadening the resonance bandwidth, we also calculated electric (|E|) and magnetic (|Hz|) distributions corresponding to different transmission dips at s2 = 20, 24, and 28 mm (see Figs. 4(a)–4(c)), respectively. Different field distributions were observed for the resonances excited at 1.52, 1.61 and 1.68 THz, respectively. It is obvious that the distribution of the electric field is not only on the gap of the structure but also on the arm of the entire structure, but it is mainly in the outer SRR) (see Figs. 4(a1)–4(c1)), which means the two parallel currents (electric resonance [ 29]) along the base line of the outer SRR and a loop current (magnetic resonance) along the arm of the inner SRR (see the distribution of the magnetic field in Figs. 4(a2)–4(c2)), respectively. Besides, the strength of the magnetic resonance gradually decreases with the increases of the s2, as shown in Figs. 4(a2)–4(c2). Obviously, by further increasing the distance s2 or decrease the arm length of the inner SRR, the electric and magnetic distributions are essentially different from those of s2 = 4, 8, and 12 mm. Hence, the mechanism for further broaden bandwidth is attributed to the decrease of the magnetic resonances.
In fact, for single SRR structure, the anti-parallel currents in both arms cancel each giving rise to nearly zero dipole moment. Therefore, the net dipole moment is mainly contributed from the base line of the SRR, leading to a longer base line to a broader resonance bandwidth due to the fact that the radiation damping increases with the particle size (the length of the base line) [ 30, 31]. In contrast, shorter base line or smaller distributions current, which means smaller dipole moment, along the base line of the SRR corresponds to a smaller resonance bandwidth. As the strength of the magnetic resonance or the distributions of the current along the arm of the inner SRR gradually decreases with the s2, the radiation damping of the structure will be increased because the strength of the electric resonance is not substantially changing as the s2 increased, thus, it results in the broadening of the resonance bandwidth.
Having studied the mechanism of the broadening of the resonance bandwidth, the effects of the changes in the separation between the two SRRs (s1) and the period of this proposed structure (P) on the spectral resonance of this structure was investigated. The s1 ranging from 12 to 4 mm along the x-axis direction form an arithmetic series, and the difference = −4 mm. In fact, when the value of s2 is less than 12 mm, the effective inductance of the entire structure gradually decreases with the decrease of s1. Therefore, the gradually decreased s1 enables narrowing and a red shift of the LC resonance (see Fig. 5(a)). Similarly, for the s2 larger than 20 mm, due to the strength of the magnetic resonance gradually increases with the decrease of the s1, its resonance bandwidth and frequency is still narrowed and red shift with the decrease of the s1, respectively (see Fig. 5(b)). Figures 5(a) and 5(b) show the dependence of the spectral resonance of the proposed structure with the change of the s1 for s2 = 4 and 28 mm, respectively. It is obvious that the resonance bandwidth undergoes narrowing and resonance frequency appears red shift with the decrease of s1.
Furthermore, the size of the period P is also critical to obtain the broaden resonance bandwidth because the changes in P can significantly influence the near-field interaction of neighboring cells (see the distribution of the electric field in Figs. 4(a1)–4(c1)) and consequently modify the property of the resonance bandwidth. Figure 5(c) shows the influence of the period P on the resonance bandwidth. It shows that the resonance bandwidth gradually increases with the decrease of the period P. The resonance bandwidth increased dramatically from 0.49 to 1.26 THz as the P ranged from= 85 to 55 mm, and the bandwidth enhanced by 2.6 times. Very importantly, its resonance bandwidth is 18.9 times larger than that of the outer SRR. The increase of the resonance bandwidth could have potential applications in development of planar broadband terahertz photonic devices.
Conclusions
In conclusion, we reported a simple design of broadband filter composed of two nested SRRs. Our simulated results showed that the bandwidth broadened by 7.4 times without altering the resonance minima significantly. The broadened resonance bandwidth can be explained by two different resonance mechanisms, and its resonance bandwidth can be changed other geometrical parameters. Particularly, the bandwidth of the designed structure was about 18.9 times larger than that of the original single SRR structure when the period was decreased. The designing concept of this proposed structure could be readily extended to other frequency regimes for a host of applications such as detection, imaging and solar cell.